We followed the standard training strategy to train our cGAN[1]}: we updated the parameters of \(D\)  and \(G\)  alternatively per gradient descent step. We used the Adam optimizers[2]} with an initial learning rate as \(2\times 10^{-4}\)  and momentum parameters \(\beta _{1} = 0.5\)  and \(\beta _{2} = 0.999\) . A mini-batch size of 1 was used. During training, we applied online intensity augmentationshttps://docs.monai.io/en/stable/transforms.html including random intensity shifts with an offset ranging from \([-0.1, 0.1]\)  and random contrast adjustment with gamma ranging from \([0.5, 1.5]\) . Both intensity augmentations were applied with a probability of \(0.2\) . This augmentation strategy aimed to simulate the varying intensity distributions of MRI scans, especially when they were acquired from different sites or with different protocols.
We did not augment the intensity values of CT images to preserve the physical meaning of the skull HU values. During the inference phase, we used a sliding window to generate synthetic CT patches across the whole volume and fused the results by averaging multiple predictions over each pixel. We set the overlapping ratio between the sliding windows as \(0.75\)  of the patch dimension, i.e., \(192\times 192\times 24\) . For post-processing, we obtained a skull mask from the synthetic CT image following the same steps as in pre-processing, i.e., global threshold, connected component analysis and morphological dilation. This mask was used to remove the false positive predictions outside the skull regions.
